Male Lead Falls in Love First

Natsu no Koi wa Nijiiro ni Kagayaku
Dear Sister

- A lot of "noona romances". Actually, probably almost all of them? I won't list these but there are a lot of recommendation threads you can browse through~

- In Time With You is a really good Taiwanese drama. The male lead has a long unrequited love. (There's also a Korean remake but imho, the original is far better)

- Falling for Innocence. Uh, he starts off mean but after the heart transplant thing will start acting differently. So don't turn this on down right away because of the meanie.

- Second Time Twenty Years Old. His feelings go way back whereas she married someone else. 

Reply 1997 (has actually 14 30min episodes + 2 1hr episodes if I remember well)
It's Okay, That's Love (16 ep)
Scent of a Woman (16 ep - debatable who falls in love first -or i just don't remember it well oops- but the guy is the one who's serious about their relationship first)

for all 3 of them: the character's stories have their up & downs,but It'd generally consider them happy & heart-warming stories :) Reply 1997 is very easy to watch, whereas it's okay, that's love and scent of a woman deal with more serious topics (but don't let that fool you :P)

I Hear Your Voice

I second these dramas that have been mentioned:

It's Okay, That's Love
Scent of a Woman
The Greatest Love
I Hear Your Voice
Healer
Reply 1997

But I also recommend these ones:

Marriage Contract
Reply 1988
Lucky Romance
Witch's Romance